Collisionless and Decentralized Formation Control for Strings

Multi-agent systems (MAS) have proven to be a versatile framework for studying diverse scalability problems in Science and Engineering, such as dynamic networks [35], autonomous vehicles [5], collective behaviour of humans or animals [42, 43], and many others [2, 6]. Mathematically, MAS are often modelled as large-scale dynamical systems where each agent can be considered as a subset of states, updated via interaction forces such as attraction, repulsion, alignment, etc., [27, 19] or through the optimization of a pay-off function in a control/game framework [32, 29]. In this work, we approach the study of MAS from a control viewpoint. We study a class of sparsely interconnected agents in one dimension, interacting through nonlinear couplings and a decentralized control law. The elementary building block of our approach is the celebrated Cucker-Smale model for consensus dynamics [19], which corresponds to a MAS where each agent is endowed with second-order nonlinear dynamics for velocity alignment, and where the influence of neighbouring agents decays with distance. The Cucker-Smale model and variants can represent the physical motion of agents on the real line, inspired by autonomous vehicle formations in platooning with a nearest-neighbour interaction scheme [41, 44].